A car with 60 cm diameter tires is traveling at a constant speed of 100 km/hr. What is the angular velocity of the tires in rad/s?
To find the angular velocity of the tires, we'll first need to convert the car's speed from kilometers per hour to meters per second, and then calculate the linear velocity of the tires.
Step 1: Convert the speed from km/hr to m/s.
To convert from km/hr to m/s, we need to divide the speed by 3.6 since there are 3.6 seconds in one hour.
100 km/hr / 3.6 = 27.78 m/s (rounded to two decimal places)
Step 2: Calculate the linear velocity of the tires.
The linear velocity of a point on the circumference of a circle is given by the formula:
v = ω * r
where v is the linear velocity, ω is the angular velocity, and r is the radius of the circle.
Given that the tires have a diameter of 60 cm, we can calculate the radius by dividing the diameter by 2:
radius = 60 cm / 2 = 30 cm
We need to convert the radius from centimeters to meters:
radius = 30 cm / 100 = 0.3 m
Now we can plug the values into the formula to find the linear velocity:
27.78 m/s = ω * 0.3 m
Step 3: Solve for ω.
Rearranging the equation, we get:
ω = v / r
Substituting the given values:
ω = 27.78 m/s / 0.3 m
ω ≈ 92.6 rad/s (rounded to one decimal place)
Therefore, the angular velocity of the tires is approximately 92.6 rad/s.